The aim of this study is to mathematically model the behavior of magneto-hydrodynamics (MHD) in a two-dimensional unsteady flow, specifically focusing on natural convection (NC) and heat transfer (HT) within a wavy octagonal cavity. The study investigates how heat is transferred and fluid flows within this cavity under specific conditions. In particular, it examines the impact of various parameters, such as the Hartmann number (Ha), Rayleigh number (Ra), and the volume fraction of nanoparticles (ϕ) on the flow and HT patterns. This cavity includes a rectangular vertical wall (RVW) at the center of its bottom wall, filled with kerosene-TiO2 nanofluid of spherical shape. Within this setup, the RVW is maintained at a high temperature (T = Th), while the wavy wall is kept at a lower temperature (T = Tc, where Tc <Th). All other boundaries of the domain are assumed to be adiabatic. The finite element method (FEM) is employed as the solver for the relevant partial differential equations in numerical simulations. The results show excellent agreement with previously published research papers. The numerical solution transitions from an unsteady state to a steady state in approximately 0.68 dimensionless time units during the HT process. Throughout the study, various parameters are explored, including Ha, ranging from 0 to 100, Ra, ranging from 103 to 106, and ϕ, ranging from 0 to 0.05. The findings reveal distinct patterns in streamlines and isotherms. Specifically, a reduction in the rate of HT is observed as the Lorentz force increases, while the rate of HT is enhanced with increasing buoyancy force. Additionally, an expansion in ϕ led to an increase in the rate of HT. The study's findings could contribute to our understanding of fluid dynamics, heat transfer, and the behavior of nanofluids in complex geometries, potentially leading to improvements in various engineering and industrial applications.

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